Dice notation
3d729
- 3d729
- 3 to 2187
- mean 1,095
- mode 1095
Rolling 3d729 gives a total between 3 and 2,187, with a mean of 1,095 and a standard deviation of 364.4997. There are 387,420,489 equally likely ordered outcomes, and the most likely total is 1,095 at 0.103%.
The roll
Notation3d729
Dice3
Faces per die729
Minimum total3all 3 dice showing 1
Maximum total2,187all 3 dice showing 729
Distinct totals2,185
Mean1,095n(f + 1)/2 + modifier, exact
Variance132,860n(f² − 1)/12, exact
Standard deviation364.49965706≈
Counting the outcomes
Ordered outcomes387,420,489729^3, every die distinguishable
Most likely total1,095
Chance of that total0.102881%≈
Ways to roll it398,581exact count
Chance of the minimum2.58117479 × 10^-7%≈1 in 387,420,489
Chance of the maximum2.58117479 × 10^-7%≈1 in 387,420,489
Shape of the distribution
2,185 distinct totals, too many to list individually.
1st percentile287≈1.006% of rolls are this or lower
5th percentile490≈5.03% of rolls are this or lower
25th percentile838≈25.063% of rolls are this or lower
50th percentile1,095≈50.051% of rolls are this or lower
75th percentile1,352≈75.023% of rolls are this or lower
95th percentile1,700≈95.001% of rolls are this or lower
99th percentile1,903≈99.004% of rolls are this or lower
Chance of rolling at least
22199.5482%≈
54992.9591%≈
1,09550.0514%≈
1,6417.0796%≈
1,9690.4581%≈
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